Given:

The region bounded by:

$y=(\frac{1}{x})$

$y=(1-x)$

$x=\frac{1}{2}$

$x=4$

NOTE: All Dimensions are inches, unless noted otherwise.

Find:

Using integration $($manual hand calculations$),$ calculate the values for the following problems.

You shall show all calculations needed to arrive at each answer.

Submitted responses shall be to $4$ significant figures. Do NOT use scientific notation.

The Area of the region is

$i{n}^2.$

The Centroid of the region has an $x-$coordinate of

in$.$

The Centroid of the region has a $y-$coordinate of

in$.$

The Area Moment of Inertia of the region about the $x-$axis is

in $^4.$

The Area Moment of Inertia of the region about the $y-$axis is

in ${?}^4$

The Area Moment of Inertia of the region about the centroidal x$-$axis is

in ${?}^4.$

The Area Moment of Inertia of the region about the centroidal $y-$axis is

in ${?}^4.$